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A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.?
Verified Answer
A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.sm...
let the total mass of the bomb be "4m"
so 4 m = 12 kg
m = 12/4
m = 3 kg
since the ratio of pieces of masses is 1 :3
m₁ = mass of smaller piece = m = 3 kg
m₂ = mass of larger piece = 3 m = 3 x 3 = 9 kg
v₁ = velocity of smaller piece
v₂ = velocity of larger piece
initially the bomb was at rest , hence initial total momentum = 0
Using conservation of momentum
Final total momentum = initial total momentum
m₁ v₁ + m₂ v₂ = 0
m v₁ + (3 m) v₂ = 0
v₁ + 3 v₂ = 0
v₁ = - 3 v₂ eq-1
Given that : initial kinetic energy = 216
we know that : kinetic energy = (0.5) mv^2 where m = mass , v = speed
so
(0.5) m₁ v₁^2= 216
(3) v₁^2 = 432
v₁ = 12 m/s
using eq-1
v₁ = - 3 v₂
12 = - 3 v₂
v₂ = - 4 m/s
Momentum of the larger piece is given as
P₂ = m₂ v₂ = 9 (-4) = - 36 kgm/s
This question is part of UPSC exam. View all NEET courses
Most Upvoted Answer
A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.sm...
Explanation:
Given:
- Mass of the bomb (m) = 12 kg
- Ratio of masses of fragments = 1:2
- Kinetic energy of smaller fragment = 216 J
Calculating masses of the fragments:
- Let the masses of the fragments be m1 and m2, such that m1:m2 = 1:2
- Using the ratio, we can write:
m1 = x and m2 = 2x
- Given that the total mass is 12 kg:
m1 + m2 = 12
x + 2x = 12
3x = 12
x = 4 kg
- Therefore, the masses of the fragments are:
m1 = 4 kg and m2 = 8 kg
Calculating the kinetic energy of the heavier fragment:
- Given that the kinetic energy of the smaller fragment is 216 J, the total kinetic energy of the fragments is the same.
- Let the kinetic energy of the heavier fragment be K.
K + 216 = Total kinetic energy
K + 216 = 216 + K
K = 0 J
- This implies that the heavier fragment has no kinetic energy.
Calculating the momentum of the heavier fragment:
- The total momentum before the explosion is zero.
- Let the momentum of the heavier fragment be p2.
- Using the principle of conservation of momentum:
m1v1 + m2v2 = 0
4v1 + 8v2 = 0
4v1 = -8v2
v1 = -2v2
- The momentum of the heavier fragment (p2) is given by:
p2 = m2 * v2
p2 = 8 * v2
- Since v1 = -2v2, we have:
p2 = 8 * (-v1/2)
p2 = -4 * v1
Therefore, the momentum of the heavier fragment is -4 times the momentum of the smaller fragment.
Given:
- Mass of the bomb (m) = 12 kg
- Ratio of masses of fragments = 1:2
- Kinetic energy of smaller fragment = 216 J
Calculating masses of the fragments:
- Let the masses of the fragments be m1 and m2, such that m1:m2 = 1:2
- Using the ratio, we can write:
m1 = x and m2 = 2x
- Given that the total mass is 12 kg:
m1 + m2 = 12
x + 2x = 12
3x = 12
x = 4 kg
- Therefore, the masses of the fragments are:
m1 = 4 kg and m2 = 8 kg
Calculating the kinetic energy of the heavier fragment:
- Given that the kinetic energy of the smaller fragment is 216 J, the total kinetic energy of the fragments is the same.
- Let the kinetic energy of the heavier fragment be K.
K + 216 = Total kinetic energy
K + 216 = 216 + K
K = 0 J
- This implies that the heavier fragment has no kinetic energy.
Calculating the momentum of the heavier fragment:
- The total momentum before the explosion is zero.
- Let the momentum of the heavier fragment be p2.
- Using the principle of conservation of momentum:
m1v1 + m2v2 = 0
4v1 + 8v2 = 0
4v1 = -8v2
v1 = -2v2
- The momentum of the heavier fragment (p2) is given by:
p2 = m2 * v2
p2 = 8 * v2
- Since v1 = -2v2, we have:
p2 = 8 * (-v1/2)
p2 = -4 * v1
Therefore, the momentum of the heavier fragment is -4 times the momentum of the smaller fragment.
Community Answer
A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.sm...
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A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.?
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A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.?.
A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bomb of mass 12 kg explodes into 2 fragments of mass in ratio 1:2.smaller fragment have kinetic energy 216J.the momentum of heavier fragment is.?.
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